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7. The drawing of tangents to circles, under various
about circles; and of circles in and about figures.
have been studied theoretically, but should in all
cases precede the study of the Circle in Geometry. The above constructions are to be taught generally, and illustrated by one or more of the following classes of problems :
(a) The making of constructions involving various com
binations of the above in accordance with general
lie on a straight line.
nations of them to scale (but without the protractor).
indirect measurement of distances.
the application of these to the laying off of angles,
[NOTE.—In the following Introduction are collected together certain general axioms which, though frequently used in Geometry, are not peculiar to that science, and also certain logical relations, the distinct apprehension of which is very desirable in connexion with the demonstrations of the Propositions. They are brought together here for convenience of reference, but it is not intended to imply by this that the study of Geometry ought to be preceded by a study of the logical interdependence of associated theorems. The Association think that at first all the steps by which any theorem is demonstrated should be carefully gone through by the student, rather than that its truth should be inferred from the logical rules here laid down. At the same time they strongly recommend an early application of general logical principles.]
1. Propositions admitted without demonstration are
more frequently used.
(CORRESPONDING TO EUCLID, BOOKS I-VI.)
PREPARED BY THE
ASSOCIATION FOR THE IMPROVEMENT OF GEOMETRICAL
FOURTH EDITION, REVISED.
[All Rights reserved.]
1832. e. 1